Shannon Entropy Loss in Mixed-Radix Conversions
| dc.contributor.author | Vennos, Amy | en |
| dc.contributor.author | Michaels, Alan J. | en |
| dc.contributor.department | Hume Center for National Security and Technology | en |
| dc.date.accessioned | 2021-08-09T16:56:35Z | en |
| dc.date.available | 2021-08-09T16:56:35Z | en |
| dc.date.issued | 2021-07-27 | en |
| dc.date.updated | 2021-08-06T15:19:17Z | en |
| dc.description.abstract | This paper models a translation for base-2 pseudorandom number generators (PRNGs) to mixed-radix uses such as card shuffling. In particular, we explore a shuffler algorithm that relies on a sequence of uniformly distributed random inputs from a mixed-radix domain to implement a Fisher–Yates shuffle that calls for inputs from a base-2 PRNG. Entropy is lost through this mixed-radix conversion, which is assumed to be surjective mapping from a relatively large domain of size <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>2</mn><mi>J</mi></msup></semantics></math></inline-formula> to a set of arbitrary size <i>n</i>. Previous research evaluated the Shannon entropy loss of a similar mapping process, but this previous bound ignored the mixed-radix component of the original formulation, focusing only on a fixed <i>n</i> value. In this paper, we calculate a more precise formula that takes into account a variable target domain radix, <i>n</i>, and further derives a tighter bound on the Shannon entropy loss of the surjective map, while demonstrating monotonicity in a decrease in entropy loss based on increased size <i>J</i> of the source domain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>2</mn><mi>J</mi></msup></semantics></math></inline-formula>. Lastly, this formulation is used to specify the optimal parameters to simulate a card-shuffling algorithm with different test PRNGs, validating a concrete use case with quantifiable deviations from maximal entropy, making it suitable to low-power implementation in a casino. | en |
| dc.description.version | Published version | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Vennos, A.; Michaels, A. Shannon Entropy Loss in Mixed-Radix Conversions. Entropy 2021, 23, 967. | en |
| dc.identifier.doi | https://doi.org/10.3390/e23080967 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/104620 | en |
| dc.language.iso | en | en |
| dc.publisher | MDPI | en |
| dc.rights | Creative Commons Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject | PRNG | en |
| dc.subject | Shannon entropy | en |
| dc.subject | mixed-radix conversion | en |
| dc.title | Shannon Entropy Loss in Mixed-Radix Conversions | en |
| dc.title.serial | Entropy | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |